MinT - Information on Result #1051412

Information on Result #1051412

Linear OOA(2¹³⁸, 2097150, F₂, 4, 12) (dual of [(2097150, 4), 8388462, 13]-NRT-code), using OOA 4-folding based on linear OA(2¹³⁸, 8388600, F₂, 12) (dual of [8388600, 8388462, 13]-code), using

discarding factors / shortening the dual code based on linear OA(2¹³⁸, large, F₂, 12) (dual of [large, large−138, 13]-code), using
- the primitive narrow-sense BCH-code C(I) with length 8388607Â = 2²³âˆ’1, defining interval IÂ =Â [1,12], and designed minimum distance dÂ â‰¥Â |I|+1Â =Â 13 [i]

Mode: Constructive and linear.

Optimality

Show details for fixed k and m, k and s, k and t, m and s, m and t.

Other Results with Identical Parameters

None.

Depending Results

The following results depend on this result:

	Result		Method
1	Linear OOA(2¹⁴⁴, 2097153, F₂, 4, 12) (dual of [(2097153, 4), 8388468, 13]-NRT-code)	[i]	(u,Â u+v)-Construction for OOAs
2	Linear OOA(2¹⁴⁵, 2097155, F₂, 4, 12) (dual of [(2097155, 4), 8388475, 13]-NRT-code)	[i]
3	Linear OOA(2¹⁴⁶, 2097156, F₂, 4, 12) (dual of [(2097156, 4), 8388478, 13]-NRT-code)	[i]
4	Linear OOA(2¹⁴⁷, 2097159, F₂, 4, 12) (dual of [(2097159, 4), 8388489, 13]-NRT-code)	[i]
5	Linear OOA(2¹⁴⁸, 2097161, F₂, 4, 12) (dual of [(2097161, 4), 8388496, 13]-NRT-code)	[i]
6	Linear OOA(2¹⁴⁹, 2097165, F₂, 4, 12) (dual of [(2097165, 4), 8388511, 13]-NRT-code)	[i]
7	Linear OOA(2¹⁵⁰, 2097171, F₂, 4, 12) (dual of [(2097171, 4), 8388534, 13]-NRT-code)	[i]
8	Linear OOA(2¹⁵¹, 2097173, F₂, 4, 12) (dual of [(2097173, 4), 8388541, 13]-NRT-code)	[i]
9	Linear OOA(2¹⁵², 2097176, F₂, 4, 12) (dual of [(2097176, 4), 8388552, 13]-NRT-code)	[i]
10	Linear OOA(2¹⁵³, 2097186, F₂, 4, 12) (dual of [(2097186, 4), 8388591, 13]-NRT-code)	[i]
11	Linear OOA(2¹⁵⁴, 2097192, F₂, 4, 12) (dual of [(2097192, 4), 8388614, 13]-NRT-code)	[i]
12	Linear OOA(2¹⁵⁵, 2097198, F₂, 4, 12) (dual of [(2097198, 4), 8388637, 13]-NRT-code)	[i]
13	Linear OOA(2¹⁵⁶, 2097214, F₂, 4, 12) (dual of [(2097214, 4), 8388700, 13]-NRT-code)	[i]
14	Linear OOA(2¹⁵⁷, 2097222, F₂, 4, 12) (dual of [(2097222, 4), 8388731, 13]-NRT-code)	[i]
15	Linear OOA(2¹⁵⁸, 2097229, F₂, 4, 12) (dual of [(2097229, 4), 8388758, 13]-NRT-code)	[i]
16	Linear OOA(2¹⁵⁹, 2097277, F₂, 4, 12) (dual of [(2097277, 4), 8388949, 13]-NRT-code)	[i]
17	Linear OOA(2¹⁶², 2097280, F₂, 4, 12) (dual of [(2097280, 4), 8388958, 13]-NRT-code)	[i]
18	Linear OOA(2¹⁶³, 2097403, F₂, 4, 12) (dual of [(2097403, 4), 8389449, 13]-NRT-code)	[i]
19	Linear OOA(2¹⁶⁴, 2097404, F₂, 4, 12) (dual of [(2097404, 4), 8389452, 13]-NRT-code)	[i]
20	Linear OOA(2¹⁶⁶, 2097659, F₂, 4, 12) (dual of [(2097659, 4), 8390470, 13]-NRT-code)	[i]
21	Linear OOA(2¹⁶⁷, 2097660, F₂, 4, 12) (dual of [(2097660, 4), 8390473, 13]-NRT-code)	[i]
22	Linear OOA(2¹⁶⁹, 2098171, F₂, 4, 12) (dual of [(2098171, 4), 8392515, 13]-NRT-code)	[i]
23	Linear OOA(2¹⁷⁰, 2098172, F₂, 4, 12) (dual of [(2098172, 4), 8392518, 13]-NRT-code)	[i]
24	Linear OOA(2¹⁷², 2099197, F₂, 4, 12) (dual of [(2099197, 4), 8396616, 13]-NRT-code)	[i]
25	Linear OOA(2¹⁷⁵, 2101243, F₂, 4, 12) (dual of [(2101243, 4), 8404797, 13]-NRT-code)	[i]
26	Linear OOA(2¹⁷⁶, 2101244, F₂, 4, 12) (dual of [(2101244, 4), 8404800, 13]-NRT-code)	[i]
27	Linear OOA(2¹⁷⁸, 2105341, F₂, 4, 12) (dual of [(2105341, 4), 8421186, 13]-NRT-code)	[i]
28	Linear OOA(2¹⁸¹, 2113531, F₂, 4, 12) (dual of [(2113531, 4), 8453943, 13]-NRT-code)	[i]
29	Linear OOA(2¹⁸², 2113532, F₂, 4, 12) (dual of [(2113532, 4), 8453946, 13]-NRT-code)	[i]
30	Linear OOA(2¹⁸⁴, 2129915, F₂, 4, 12) (dual of [(2129915, 4), 8519476, 13]-NRT-code)	[i]
31	Linear OOA(2¹⁸⁵, 2129916, F₂, 4, 12) (dual of [(2129916, 4), 8519479, 13]-NRT-code)	[i]
32	Linear OOA(2¹⁸⁷, 2162683, F₂, 4, 12) (dual of [(2162683, 4), 8650545, 13]-NRT-code)	[i]
33	Linear OOA(2¹⁸⁸, 2162684, F₂, 4, 12) (dual of [(2162684, 4), 8650548, 13]-NRT-code)	[i]
34	Linear OOA(2¹⁹⁰, 2228221, F₂, 4, 12) (dual of [(2228221, 4), 8912694, 13]-NRT-code)	[i]
35	Linear OOA(2¹⁹³, 2359291, F₂, 4, 12) (dual of [(2359291, 4), 9436971, 13]-NRT-code)	[i]
36	Linear OOA(2¹⁹⁴, 2359292, F₂, 4, 12) (dual of [(2359292, 4), 9436974, 13]-NRT-code)	[i]
37	Linear OOA(2¹⁹⁶, 2621437, F₂, 4, 12) (dual of [(2621437, 4), 10485552, 13]-NRT-code)	[i]
38	Linear OOA(2¹⁹⁹, 3145723, F₂, 4, 12) (dual of [(3145723, 4), 12582693, 13]-NRT-code)	[i]
39	Linear OOA(2²⁰⁰, 3145724, F₂, 4, 12) (dual of [(3145724, 4), 12582696, 13]-NRT-code)	[i]
40	Linear OOA(2²⁰², 4194299, F₂, 4, 12) (dual of [(4194299, 4), 16776994, 13]-NRT-code)	[i]
41	Linear OOA(2²⁰³, 4194300, F₂, 4, 12) (dual of [(4194300, 4), 16776997, 13]-NRT-code)	[i]
42	Linear OOA(2¹⁶³, 2097404, F₂, 4, 12) (dual of [(2097404, 4), 8389453, 13]-NRT-code)	[i]
43	Linear OOA(2¹⁶⁶, 2097660, F₂, 4, 12) (dual of [(2097660, 4), 8390474, 13]-NRT-code)	[i]
44	Linear OOA(2¹⁶⁹, 2098172, F₂, 4, 12) (dual of [(2098172, 4), 8392519, 13]-NRT-code)	[i]
45	Linear OOA(2¹⁷⁵, 2101244, F₂, 4, 12) (dual of [(2101244, 4), 8404801, 13]-NRT-code)	[i]
46	Linear OOA(2¹⁸¹, 2113532, F₂, 4, 12) (dual of [(2113532, 4), 8453947, 13]-NRT-code)	[i]
47	Linear OOA(2¹⁸⁴, 2129916, F₂, 4, 12) (dual of [(2129916, 4), 8519480, 13]-NRT-code)	[i]
48	Linear OOA(2¹⁸⁷, 2162684, F₂, 4, 12) (dual of [(2162684, 4), 8650549, 13]-NRT-code)	[i]
49	Linear OOA(2¹⁹³, 2359292, F₂, 4, 12) (dual of [(2359292, 4), 9436975, 13]-NRT-code)	[i]
50	Linear OOA(2¹⁹⁹, 3145724, F₂, 4, 12) (dual of [(3145724, 4), 12582697, 13]-NRT-code)	[i]
51	Linear OOA(2²⁰², 4194300, F₂, 4, 12) (dual of [(4194300, 4), 16776998, 13]-NRT-code)	[i]
52	Linear OOA(2¹³⁸, 1956549, F₂, 5, 12) (dual of [(1956549, 5), 9782607, 13]-NRT-code)	[i]	Embedding of OOA with Gilbertâ€“VarÅ¡amov Bound
53	Linear OOA(2¹³⁸, 1956549, F₂, 6, 12) (dual of [(1956549, 6), 11739156, 13]-NRT-code)	[i]
54	Linear OOA(2¹³⁸, 1956549, F₂, 7, 12) (dual of [(1956549, 7), 13695705, 13]-NRT-code)	[i]
55	Linear OOA(2¹³⁸, 1956549, F₂, 8, 12) (dual of [(1956549, 8), 15652254, 13]-NRT-code)	[i]
56	Digital (126, 138, 1956549)-net over F₂	[i]